All Questions
Tagged with motivation soft-question
9 questions
123
votes
18
answers
14k
views
How do you decide whether a question in abstract algebra is worth studying?
Dear MO-community, I am not sure how mature my view on this is and I might say some things that are controversial. I welcome contradicting views. In any case, I find it important to clarify this in my ...
57
votes
10
answers
4k
views
Books/websites which have motivating stories of mathematicians overcoming hardships in life
Edit 1: I have received a lot of great answers. I am not accepting any answer because I think there might be in future that some user want to contribute any new answer, as in my opinion some users ...
44
votes
4
answers
7k
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What motivates modern algebraic geometry for a combinatorial/constructive algebraist?
This is, basically, me trying to generalize "Why should I care for sheaves and schemes?" into a reasonable question. Whether successfully, time will tell, but let me hope that if not the question, ...
- 33.8k
34
votes
6
answers
4k
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Why study finite topological spaces?
In rereading Thurston's essay On Proof and Progress in Mathematics I ran across this passage:
… this means that some concepts that I use freely and naturally in
my personal thinking are foreign to ...
- 737
23
votes
6
answers
2k
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Are rings really more fundamental objects than semi-rings?
The discovery (or invention) of negatives, which happened several centuries ago by the Chinese, Indians and Arabs, has of course be of fundamental importance to mathematics.
From then on, it seems ...
20
votes
2
answers
1k
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Commutative rings : Topoi = Fields :?
The following is probably a bad question, but hopefully, it might have a very good answer.
In category theory there is a quite famous analogy between topoi and commutative rings, I was never ...
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16
votes
0
answers
2k
views
Why do we study symplectic geometry? [closed]
What is the motivation behind studying smooth manifolds with a non-degenerate closed two-form?
The subject certainly originated from physics, but is there a deeper reason for why it is still an ...
- 189
13
votes
4
answers
3k
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Is modern computability theory "really" about algorithms?
Apologies if my question seems overly naive, but I haven't seen/heard/read any good answers.
What is modern computability theory "really" about? The study of feasible(even remotely feasible) ...
- 141
7
votes
1
answer
543
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Are large cardinals about more than just consistency?
The other day, I was reading the preface of Kanamori's The Higher Infinite and noticed that he says large cardinals provide a useful 'measuring stick' for consistency. That raised the question of ...
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